Metamodeling of Combined Discrete/Continuous Responses

Metamodels are effective for providing fast-running surrogate approximations of product or system performance. Since these approximations are generally based on continuous functions, they can provide poor fits of discontinuous response functions. Many engineering models produce functions that are only piecewise continuous, due to changes in modes of behavior or other state variables. In this paper we investigate the use of a state-selecting metamodeling approach that provides an accurate approximation for piecewise continuous responses. The proposed approach is applied to a desk lamp performance model. Three types of metamodels— quadratic polynomials, spatial correlation (kriging) models, and radial basis functions—and five types of experimental designs—full factorial designs, D-best Latin hypercube designs, fractional Latin hypercubes, Hammersley sampling sequences, and uniform designs—are compared based on three error metrics computed over the design space. The state-selecting metamodeling approach outperforms a combined metamodeling approach in this example, and radial basis functions perform well for metamodel construction.